Re: FixedPoint[Cos, 1.0]

*To*: mathgroup at smc.vnet.net*Subject*: [mg119409] Re: FixedPoint[Cos, 1.0]*From*: Dana DeLouis <dana.del at gmail.com>*Date*: Thu, 2 Jun 2011 07:16:28 -0400 (EDT)

Hi. I remember this use to work as per the documentation example in earlier versions. As others have mentioned, the values cycle. FixedPointList[Cos,1.0,91][[-3;;]]//FullForm List[0.7390851332151605`,0.7390851332151608`,0.7390851332151605`] Perhaps an alternative... NestWhile[Cos[#]&,1.0,UnsameQ,All]//FullForm 0.7390851332151605` If we add an extra 2 loops (1000 for safety or max loops) we see the same cycle. t=NestWhileList[Cos[#]&,1.0,UnsameQ,All,1000,2]; t[[-3;;]]//FullForm List[0.7390851332151605`,0.7390851332151608`,0.7390851332151605`] = = = = = = = = = = HTH : >) Dana DeLouis Mac, Math 8 On May 31, 7:49 am, J Siehler <jsieh... at gmail.com> wrote: > My numerical analysis students this past term pointed out to me that > the command > > FixedPoint[Cos, 1.0] > > which is the first example in the Information for FixedPoint doesn't > ever finish running (or, not in any reasonable amount of time). We > tried this on serveral versions of Mathematica (6.x, 7.x, and 8.x), > all on OS X, and got the same nonresult. > > It can be forced by specifying something like FixedPoint[Cos, 1.0, > SameTest -> (Abs[#1 - #2] < 10^-10 &)] or FixedPoint[Cos, 1.0, 40], > but it seems like that should be unnecessary, and the form given in > the documentation should work. Can anybody else confirm this > behavior? Am I missing something totally obvious here?